In discussing the prior art, reference is made to, for example, the field of color recipe prediction for preparing a color of a particular specification by mixing a plurality of pigments. In the description that follows, original pigments to be mixed to produce the color of the particular specification are referred to as elements. The simplest prior art method for this purpose is that an expert empirically determines the proportion or mixing ratio of the elements to be mixed, by looking at the target color. Another prior art method comprises the steps of analyzing a spectrum of the target color, making a search in a database to find a color which may match with the color of a spectrum closest to the spectrum previously analyzed, and finely adjusting the proportion of the elements making reference to the proportion of the element pigments that has been used to produce the previous color.
A further prior art method is disclosed by, for example, G. Wyszecki and W. S. Stiles in their "Color Science: Concepts and Methods, Quantitative Data and Formula" (New York, N.Y.: Wiley, 2nd ed. (1982)), in which a model mathematically simulating the relationship between the color spectrum and the projected image of the proportion, such as represented by the Kubelka-Munk theory is utilized to determine the proportion from the color spectrum. A more recent prior art method is disclosed by, for example, J. M. Bishop, M. J. Bushnell and S. Westland in their "Application of Neural Networks to Computer Recipe Prediction" (Color Research and Application, Vol. 16, No. 1, pp.3-9, (1991), in which the neural network is taught to output the proportion in response to input of the color spectrum.
In any event, according to the prior art, the element pigments are mixed together according to the proportion so obtained to produce the target color.
While the foregoing discussion is directed to the color recipe, a similar discussion equally applies to the field of perfumery, preparation of food items, design of sound effects, material development or the like.
All of the prior art methods have a common feature in that a color, light or material that satisfies a given specification is produced on a trial and error basis with the use of human sensory perception, experiences and experimental data bases. It will readily be understood that it is not easy to attain high accuracy.
The mathematically simulated model represented by the equations set forth in the Kubelka-Munk theory which is generally used in the field of color recipe is limited in its application since it is difficult to prepare the model that meets all available conditions. Although the conventional Kubelka-Munk theory is widely used in predicting color matches, some assumptions are made which limit the situations where the theory may be applied. It is indeed very difficult to configure a model that supersede the above discussed model.
The utilization of the neural network appears to be an effective technique to remove the difficulty in configuring the substitute model. However, the human vision is too sensitive to allow the neural network to exhibit a required accuracy in predicting small proportions as low as 0.01%.